Evaluate the following functions : ( x) x d x - Vidyadip

Question

Evaluate the following functions : $\int \frac{\cot (\log x)}{x} \cdot d x$

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Answer

$
\begin{aligned}
& \text { Let } \mathrm{I}=\int \frac{\cot (\log x)}{x} \cdot d x \\
& \text { put } \log x=t \\
& \therefore \frac{1}{x} \cdot d x=1 \cdot d t \\
& =\int \cot t \cdot d t \\
& =\log (\sin t)+c \\
& =\log (\sin \log x)+c \\
&
\end{aligned}
$

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